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A New Result in Form of Finite Triple Sums for a Series from Ramanujan's Notebooks
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Swedish Institute of Space Physics, Uppsala Division.ORCID iD: 0000-0003-2647-8259
Univ Bonn, Phys Inst, D-53115 Bonn, Germany..
2022 (English)In: Symmetry, E-ISSN 2073-8994, Vol. 14, no 6, article id 1090Article in journal (Refereed) Published
Abstract [en]

We consider a function g(r, x, u) with x, u is an element of C and r is an element of N, which, over a symmetric domain, equals the sum of an infinite series as noted in the 16th Entry of Chapter 3 in Ramanujan's second notebook. The function attracted new attention since it was established to be closely connected to the theory of labelled trees. However, to the best of our knowledge, a closed-form solution allowing, e.g., the rapid computation of g (r, x, u) in Mathematica without explicit use of recursions has been lacking until now. Our proposed formula transforms the part depending on the variable u into a more symmetric form, which then appears inside a finite triple sum consisting of binomials and Stirling numbers of the second kind.

Place, publisher, year, edition, pages
MDPI AG , 2022. Vol. 14, no 6, article id 1090
Keywords [en]
Ramanujan, Stirling numbers, combinatorics
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-480279DOI: 10.3390/sym14061090ISI: 000817651500001OAI: oai:DiVA.org:uu-480279DiVA, id: diva2:1682156
Available from: 2022-07-08 Created: 2022-07-08 Last updated: 2022-07-08Bibliographically approved

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Vigren, Erik

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